Moto X (1st gen) 5.1 Lollipop: Does the wave-to-wake sensor work the same in Lollipop?

It works for me, too -- though I don't foresee much practical value in this feature now that it requires the delay. I'd prefer to just lift or jiggle the phone for an immediate response rather than hold my hand over the phone for 5 seconds waiting for the time/notification to appear.

GOOD news!
It is possible to get most if not all pre-Lollipop features back. In my opinion Lollipop just sucks. Not just on Motorola Moto X. It was a huge step back but most people get horny of new major updates and only use their phones for social media.

Full explanation here: I am unfortunately not allowed to post URLs. Please google: "How to get pre-Lollipop features back", first hit on XDA.
I can say I have never been happier! It did cost me half a Sunday.

If you just want Wave-to-Wake back, you need Tasker. There is a link to a Google+ post explaining it in detail, find the link in the topic on XDA. it absolutely works! There also is a video to demo the solution.

Also you can have Black Material Design apps and the HTC Sense Launcher which is great in combination with the OLED screen (better battery life) and easier on the eyes. It's all explained in the topic.

It works for me, too -- though I don't foresee much practical value in this feature now that it requires the delay. I'd prefer to just lift or jiggle the phone for an immediate response rather than hold my hand over the phone for 5 seconds waiting for the time/notification to appear.

Installed PitchBlack theme and got the Ambient display and Double Tap to sleep option enabled in CM13, which was previously disabled.